As is well known, methods of determining whether or not there is a fault in a conducting wire and detecting a distance to fault (DTF) using a reflected wave generally include time domain reflectometry (TDR), frequency domain reflectometry (FDR), and so on.
In TDR, a pulse signal or a step signal is applied to one end of a target conducting wire as a reference signal, and whether or not there is a fault is determined according to the phases of a reflected signal and the reference signal at a DTF in the conducting wire, that is, at a position at which the characteristic impedance of the conducting wire is discontinuous. Also, a delay between the reference signal and a reflected signal is measured to calculate the DTF. This method has a drawback in that a measurement error increases when the rising time of the reference signal is increased to improve resolution.
FDR has two methods. According to a first method, whether or not there is a fault in a conducting wire and a DTF are determined from a peak and a null of a standing wave generated when a sine wave applied as a reference signal and having a fixed frequency band is combined with a signal reflected by a faulty portion of the conducting wire. The resolution and the maximum measurement distance of this method are limited according to frequency sweeping and a frequency bandwidth. Also, this method is sensitive to noise and thus has low accuracy and reliability in detecting a fault in a conducting wire.
According to a second method of FDR, a mismatch point is detected by estimating a channel characteristic and an impulse response of a cable, so that a DTF in the cable is estimated. According to this method, it is possible to maintain a high signal-to-noise ratio (SNR) while using a relatively low power amplifier. Also, a measurement time can lengthen, and thus it is possible to maintain a measurement error and the resolution at desired levels.
FIG. 1 is a block diagram of a general apparatus for measuring a reflected wave which can be applied to FDR. As shown in FIG. 1, an apparatus for measuring a reflected wave which can be applied to FDR mixes an oscillation signal having a center frequency of 1.8 GHz, for example, a carrier frequency of a long term evolution (LTE) system generated by a local oscillator (LO), with a baseband sine signal having been subjected to up-conversion, for example, a measurement frequency signal (RF source) belonging to 20 MHz which is the band of use in the case of the LTE system, using a mixer to output only a baseband sine signal, performs analog-to-digital (A/D) conversion on the baseband sine signal at a predetermined sampling rate, and then estimates a reflection coefficient.
The estimated frequency-domain reflection coefficient is subsequently converted into time-domain information, and it is possible to detect a DFT by finding a time point at which a mismatch has occurred in the time-domain information. Existing measurement of a reflected wave can be generally performed using Equation 1 below.y(n)=ΓMx(n)+w(n), n=1 . . . N  [Equation 1]
In Equation 1 above, x(n) denotes a forward coupling signal, y(n) denotes a reverse coupling signal, and w(n) denotes noise inevitably generated by a coupler and so on. An optimal solution for estimating ΓA can be calculated by the least square method as Equation 2 below.
                              Y          =                                    X              ⁢                                                          ⁢              Γ                        +            W                          ⁢                                  ⁢                              YX            H                    =                                                    XX                H                            ⁢                                                          ⁢              Γ                        +                          WX              H                                      ⁢                                  ⁢                              Γ            M                    =                                                    YX                H                            ⁢                              /                            ⁢                              XX                H                                      =                                          Σ                ⁢                                                                  ⁢                                  y                  ⁡                                      (                    n                    )                                                  ⁢                                                      x                    ⁡                                          (                      n                      )                                                        *                                                            Σ                ⁢                                                                  ⁢                                  x                  ⁡                                      (                    n                    )                                                  ⁢                                                      x                    ⁡                                          (                      n                      )                                                        *                                                                    ⁢                                  ⁢                              X            =                                          [                                                      x                    ⁡                                          (                      1                      )                                                        ⁢                                                                          ⁢                  …                  ⁢                                                                          ⁢                                      x                    ⁡                                          (                      n                      )                                                                      ]                            T                                ,                      ;                          forward              ⁢                                                          ⁢              signal              ⁢                                                          ⁢              vector                                      ⁢                                  ⁢                              Y            =                                          [                                                      y                    ⁡                                          (                      1                      )                                                        ⁢                                                                          ⁢                  …                  ⁢                                                                          ⁢                                      y                    ⁡                                          (                      n                      )                                                                      ]                            T                                ,                      ;                          reverse              ⁢                                                          ⁢              signal              ⁢                                                          ⁢              vector                                      ⁢                                  ⁢                              W            =                                          [                                                      w                    ⁡                                          (                      1                      )                                                        ⁢                                                                          ⁢                  …                  ⁢                                                                          ⁢                                      w                    ⁡                                          (                      n                      )                                                                      ]                            T                                ;                      noise            ⁢                                                  ⁢            vector                                              [                  Equation          ⁢                                          ⁢          2                ]            
In Equation 2 above, XH denotes a conjugate transpose, that is, a Hermitian operator. Meanwhile, to improve the accuracy of measuring ΓA, it is very important to make the term “WXH” close to zero in Equation 2 by reducing as much influence of noise as possible using an average obtained from a large enough number of measurement values.
A cable fault may be remarkably shown at a specific frequency. Therefore, to accurately find the fault, it is necessary to use up to 1000 or more measurement frequencies over the whole area of a frequency band to be actually used.
In other words, according to an existing apparatus for detecting a cable fault, a process of collecting a reflection coefficient using one measurement frequency at a time is repeated up to 1000 or more times. Also, due to a process of changing and stabilizing a measurement frequency and a need for a sufficient measurement time to ensure the reliability of measurement, it takes a very long time to detect a cable fault.
This work was supported by the ICT R&D program of MSIP/IITP, Republic of Korea. [14-911-01-003, Development of software-based measuring equipment for enhancing inspection of radio station]